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100 80 60 40 20 0 90% deionization 100 200 300 99% deionization 100 200 300 increase h p increase H decrease L Figure 10: The specific energy consumption E for 90% deionization and 99% deionization of 10 mM NaCl solution by shock ED. For each case, the feed flow rate Q and one parameter of hp, H, and L are changed relative to the base case, while QL/h2pH is kept as a constant. To begin with, we compare the overlimiting conductance. Note that for the case of Q = 152μL/min, experimental data [8] for I ̃ > 2 are not available and thus not shown in Fig.5. As we can see, the experimental overlimiting conductance is much larger than the theoretical surface conductance κsc. With the consideration of hydronium transport and electroosmotic vortices, the DAfull model predicts very close results to the experimental data except for the case of 100 mM, when the magnitude of current is much larger than other cases and the membrane may lose some selectivity in experiments. We can also conclude that electroosmotic vortices or hydronium transport contributes more to the conductance for higher inlet concentrations and smaller flow rates. F F −3 flow rates favor deionization, and c ̃ first decreases rapidly and then reaches a plateau at about 1 × 10 F ̃ for the cases of 1 mM and 100 mM. The c ̃ is smallest at medium concentration at I = 4, which could be explained by the facts that c ̃s is large for small feed concentration and the membrane loses selectivity for high concentration, which disfavor deionization. We also expect shock ED to have slightly better deionization of NaCl compared with KCl at high current, which is not apparent in experiments. On the other hand, the DAfull model overestimates the water recovery. One possible reason is that the heterogeneous porous structure of the frit is important for the electroosmotic flow [36], which is not captured by our planar shock ED model. 3.2.3. Optimization and scale-up In this part, we first give a primary investigation on how to optimize the shock ED process in terms of specific energy consumption and deionization, based on the current prototype design. Four new parameters are investigated here: the surface charge σ, the pore size hp, and the length L and the width H of the charged channels (porous material in experiments). We change each parameter twice based on the base case, and get 8 new cases. The scaled overlimiting conductance, fresh concentration, and water recovery for these new As shown in Fig.6(b), the DAfull model provides good predictions for the fresh concentration c ̃ . For I ̃ < 1, almost all the cases converge to a single line. For I ̃ > 1, the model and experiments show that high cases are shown in Fig.7 and 8. The flow rate cases in Sec.3.2.2 are also re-visited in this part. The E at F these two deionization levels (1 − c ̃ ) along with the above five parameters is shown in Fig.9. It turns out that the pumping energy represents less than 10% of the total energy consumed at 90% deionization, and less than 2% at 99% deionization. So the electrical energy dominates energy consumption. In addition, the specific electrical energy consumption scales as IV/ωQ ∼ I ̃2Q/ωκscκ ̃ at over-diffusion-limiting current with a constant prefactor for all the cases considered in this part. As we can see in Fig.9, if the aim is to remove 90% ions, we should choose more negative σ, smaller hp, H, Q, and larger L to reduce the specific energy consumption. The main reason is that 90% deionization is obtained at around I ̃ = 1 for all the cases (see Fig.6, 8), while the above parameter set leads to smaller I ̃2Q/ωκscκ ̃ (recall that κsc ∼ |σ|L and see Fig.7 for Hhp κ ̃ and Fig.8 for ω). However, if we aim to remove 99% ions (obtained at I ̃ > 2), the trends can be different. 15PDF Image | Theory of shock electrodialysis
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